Kakuro

Kakuro Sum 3 — All 2-Cell Combinations

Updated June 10, 2026  ·  2 min read

A 2-cell Kakuro run with a clue of 3 has 1 valid combination. Each cell must contain a unique digit from 1 to 9, no repeats.

Forced combination. A 2-cell run summing to 3 can only use digits 1, 2. Both values are fixed — only their order within the run remains.

Valid combinations

Digits (any order)Sum
1 + 2= 3

What you know immediately

The digits 1, 2 appear in every valid combination — certain in this run regardless of which combination applies.

Digits 3, 4, 5, 6, 7, 8, 9 never appear in any valid combination — eliminate them immediately from all intersecting clues.

Why this clue is special

A clue of 3 over two cells is one of the four "magic" 2-cell clues in Kakuro (along with 4, 16 and 17) — the sums with exactly one valid combination. Whenever you see it, you instantly know both digits; the only question is their order, and the crossing clues decide that. The fastest read: check which crossing run can't contain a 1. A 2-cell run summing to 4 crossing one of these cells, for example, also needs a 1 — if both runs demanded the 1 in the same cell, the grid would be contradictory, so the setter's crossings always resolve it cleanly.

Solving with this clue

  1. Cross out combinations made impossible by digits already placed in the run
  2. Find digits present in all remaining combinations — those are certain placements
  3. Find digits absent from all remaining combinations — remove from intersecting clues
  4. When one combination remains, all digits in the run are determined
Use intersections: A shared cell must satisfy both its row clue and column clue. Digits that don't appear in valid combinations for either clue are eliminated. This cross-elimination often reduces options to one quickly.

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